Note that in both cases, EXIF is only one type of metadata. Other metadata sections may be present, and depending on what you want to do, both of these programs have different options for preserving some or removing it all. For example, jhead -purejpg strips all information not needed for rendering the image.

Vincent's suggestion of using exiftool is good. I suggest you write a script that accepts a single argument of a filename, and runs your desired strip functions on that. Then use find to execute this script on your file set. The script would look something like this: